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We use free probability techniques to prove that, under mild assumptions, the empirical eigenvalue distribution of $U\\Sigma V^*+A$ converges to the Brown measure of $T+a$, where $T\\in\\mathcal{A}$ is an $R$-diagonal operator freely independent from $a$ a"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2210.11147","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2022-10-20T10:25:59Z","cross_cats_sorted":["math-ph","math.MP","math.OA"],"title_canon_sha256":"322b02a3f329335179ffc22e9579dc3482a059622c2d5cbe7f2008e4ec96bf6a","abstract_canon_sha256":"f916244acb72fbec3dc168985992917986d401d4713ac50450213a2fc3fd0e34"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:48:58.768143Z","signature_b64":"8v9uMqBt//2sVx7M6E6RZjtdKUhr1yG85AGRztKgkw/2tBJQq1kdA8DKFE9NPKF0NX6j+qcA/xymFvu7d690DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"81993718e773116b799f9d036faf36b3083a1637a35b5283b8aa12608e5ae9d4","last_reissued_at":"2026-07-05T09:48:58.767619Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:48:58.767619Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Deformed single ring theorems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.OA"],"primary_cat":"math.PR","authors_text":"Ching-Wei Ho, Ping Zhong","submitted_at":"2022-10-20T10:25:59Z","abstract_excerpt":"Given a sequence of deterministic matrices $A = A_N$ and a sequence of deterministic nonnegative matrices $\\Sigma=\\Sigma_N$ such that $A\\to a$ and $\\Sigma\\to \\sigma$ in $\\ast$-distribution for some operators $a$ and $\\sigma$ in a finite von Neumann algebra $\\mathcal{A}$. 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